{
  "id": "2006.04841",
  "version": "v1",
  "published": "2020-06-08T18:04:21.000Z",
  "updated": "2020-06-08T18:04:21.000Z",
  "title": "Extreme value statistics for branching run-and-tumble particles",
  "authors": [
    "Bertrand Lacroix-A-Chez-Toine",
    "Asaf Miron"
  ],
  "comment": "14 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "physics.bio-ph"
  ],
  "abstract": "The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an evolving colony of active matter in one-dimension. In a \"persistent\" phase, the particles form macroscopic robust clusters that ballistically propagate as a whole while in an \"intermittent\" phase, particles are isolated instead. We focus our study on the fluctuations of the rightmost position $x_{\\max}(t)$ reached by time $t$ for this model. At long time, as the colony progressively invades the unexplored region, the cumulative probability of $x_{\\max}(t)$ is described by a travelling front. The transition has a remarkable impact on this front. In the intermittent phase it is qualitatively similar to the front satisfying the Fisher-KPP equation, which famously describes the extreme value statistics of the non-active branching Brownian motion. A dramatically different behaviour appears in the persistent phase, where activity imparts the front with unexpected and unusual features which we compute exactly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-08T18:04:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extreme value statistics",
      "branching run-and-tumble particles",
      "matter offer significant insight",
      "particles form macroscopic robust clusters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}